Question: The grades on a physics midterm at Almond are normally distributed with $\mu = 82$ and $\sigma = 5.5$. Stephanie earned a $68$ on the exam. Find the z-score for Stephanie's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Stephanie's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{68 - {82}}{{5.5}}} $ ${ z \approx -2.55}$ The z-score is $-2.55$. In other words, Stephanie's score was $2.55$ standard deviations below the mean.